The definition of a limit of a sequence,(adsbygoogle = window.adsbygoogle || []).push({});

if the limit is finite, is:

lim n >infinity un (un is a sequence) = l

<=>

∀ε> 0, ∃N: n > N => |un - l| < ε

This just means that un for n > N has to be a number for which: l -ε < un < l + ε

Now, I'm wondering, can't we just say:

n > N => |un -l| < kε with k a real number larger than zero?

Thanks in advance

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# B Definition of the limit of a sequence

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